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Properties

Label 3081.2
Level 3081
Weight 2
Dimension 257187
Nonzero newspaces 60
Sturm bound 1397760
Trace bound 11

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Defining parameters

Level: \( N \) = \( 3081 = 3 \cdot 13 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(1397760\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3081))\).

Total New Old
Modular forms 353184 260571 92613
Cusp forms 345697 257187 88510
Eisenstein series 7487 3384 4103

Trace form

\( 257187 q + 9 q^{2} - 375 q^{3} - 735 q^{4} + 18 q^{5} - 369 q^{6} - 740 q^{7} + 9 q^{8} - 379 q^{9} + O(q^{10}) \) \( 257187 q + 9 q^{2} - 375 q^{3} - 735 q^{4} + 18 q^{5} - 369 q^{6} - 740 q^{7} + 9 q^{8} - 379 q^{9} - 762 q^{10} + 12 q^{11} - 409 q^{12} - 855 q^{13} + 24 q^{14} - 384 q^{15} - 743 q^{16} + 18 q^{17} - 417 q^{18} - 776 q^{19} - 6 q^{20} - 406 q^{21} - 768 q^{22} + 24 q^{23} - 405 q^{24} - 747 q^{25} - 39 q^{26} - 903 q^{27} - 756 q^{28} + 30 q^{29} - 372 q^{30} - 708 q^{31} + 69 q^{32} - 354 q^{33} - 690 q^{34} + 96 q^{35} - 297 q^{36} - 654 q^{37} + 180 q^{38} - 358 q^{39} - 1494 q^{40} + 42 q^{41} - 342 q^{42} - 752 q^{43} + 132 q^{44} - 336 q^{45} - 780 q^{46} + 48 q^{47} - 357 q^{48} - 761 q^{49} + 51 q^{50} - 432 q^{51} - 945 q^{52} - 30 q^{53} - 465 q^{54} - 804 q^{55} - 466 q^{57} - 786 q^{58} + 12 q^{59} - 456 q^{60} - 798 q^{61} + 24 q^{62} - 432 q^{63} - 1347 q^{64} - 174 q^{65} - 1062 q^{66} - 1044 q^{67} - 426 q^{68} - 630 q^{69} - 1836 q^{70} - 144 q^{71} - 633 q^{72} - 926 q^{73} - 438 q^{74} - 601 q^{75} - 2016 q^{76} - 324 q^{77} - 423 q^{78} - 2541 q^{79} - 1278 q^{80} - 307 q^{81} - 1206 q^{82} - 288 q^{83} - 1038 q^{84} - 1236 q^{85} - 420 q^{86} - 492 q^{87} - 2184 q^{88} - 282 q^{89} - 540 q^{90} - 1226 q^{91} - 456 q^{92} - 588 q^{93} - 1380 q^{94} - 288 q^{95} - 729 q^{96} - 934 q^{97} + 201 q^{98} - 498 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3081))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
3081.2.a \(\chi_{3081}(1, \cdot)\) 3081.2.a.a 1 1
3081.2.a.b 1
3081.2.a.c 2
3081.2.a.d 3
3081.2.a.e 10
3081.2.a.f 15
3081.2.a.g 16
3081.2.a.h 18
3081.2.a.i 20
3081.2.a.j 21
3081.2.a.k 24
3081.2.a.l 24
3081.2.b \(\chi_{3081}(1897, \cdot)\) n/a 184 1
3081.2.c \(\chi_{3081}(1184, \cdot)\) n/a 320 1
3081.2.h \(\chi_{3081}(3080, \cdot)\) n/a 368 1
3081.2.i \(\chi_{3081}(529, \cdot)\) n/a 374 2
3081.2.j \(\chi_{3081}(1366, \cdot)\) n/a 320 2
3081.2.k \(\chi_{3081}(1186, \cdot)\) n/a 360 2
3081.2.l \(\chi_{3081}(55, \cdot)\) n/a 374 2
3081.2.m \(\chi_{3081}(2527, \cdot)\) n/a 376 2
3081.2.n \(\chi_{3081}(317, \cdot)\) n/a 728 2
3081.2.q \(\chi_{3081}(1603, \cdot)\) n/a 374 2
3081.2.r \(\chi_{3081}(419, \cdot)\) n/a 738 2
3081.2.u \(\chi_{3081}(530, \cdot)\) n/a 738 2
3081.2.v \(\chi_{3081}(1130, \cdot)\) n/a 740 2
3081.2.ba \(\chi_{3081}(1421, \cdot)\) n/a 740 2
3081.2.bf \(\chi_{3081}(2369, \cdot)\) n/a 740 2
3081.2.bg \(\chi_{3081}(238, \cdot)\) n/a 368 2
3081.2.bl \(\chi_{3081}(893, \cdot)\) n/a 738 2
3081.2.bm \(\chi_{3081}(2077, \cdot)\) n/a 374 2
3081.2.bn \(\chi_{3081}(2315, \cdot)\) n/a 640 2
3081.2.bo \(\chi_{3081}(181, \cdot)\) n/a 372 2
3081.2.br \(\chi_{3081}(56, \cdot)\) n/a 738 2
3081.2.bs \(\chi_{3081}(734, \cdot)\) n/a 1476 4
3081.2.bt \(\chi_{3081}(214, \cdot)\) n/a 748 4
3081.2.bw \(\chi_{3081}(1682, \cdot)\) n/a 1480 4
3081.2.bx \(\chi_{3081}(577, \cdot)\) n/a 744 4
3081.2.ca \(\chi_{3081}(925, \cdot)\) n/a 748 4
3081.2.cb \(\chi_{3081}(80, \cdot)\) n/a 1456 4
3081.2.cc \(\chi_{3081}(631, \cdot)\) n/a 744 4
3081.2.cd \(\chi_{3081}(371, \cdot)\) n/a 1476 4
3081.2.ci \(\chi_{3081}(196, \cdot)\) n/a 1920 12
3081.2.cj \(\chi_{3081}(428, \cdot)\) n/a 4416 12
3081.2.co \(\chi_{3081}(14, \cdot)\) n/a 3840 12
3081.2.cp \(\chi_{3081}(64, \cdot)\) n/a 2256 12
3081.2.cq \(\chi_{3081}(16, \cdot)\) n/a 4488 24
3081.2.cr \(\chi_{3081}(22, \cdot)\) n/a 4464 24
3081.2.cs \(\chi_{3081}(40, \cdot)\) n/a 3840 24
3081.2.ct \(\chi_{3081}(178, \cdot)\) n/a 4488 24
3081.2.cw \(\chi_{3081}(112, \cdot)\) n/a 4512 24
3081.2.cx \(\chi_{3081}(8, \cdot)\) n/a 8832 24
3081.2.cy \(\chi_{3081}(290, \cdot)\) n/a 8856 24
3081.2.db \(\chi_{3081}(25, \cdot)\) n/a 4464 24
3081.2.dc \(\chi_{3081}(53, \cdot)\) n/a 7680 24
3081.2.dd \(\chi_{3081}(88, \cdot)\) n/a 4488 24
3081.2.de \(\chi_{3081}(29, \cdot)\) n/a 8856 24
3081.2.dj \(\chi_{3081}(10, \cdot)\) n/a 4464 24
3081.2.dk \(\chi_{3081}(185, \cdot)\) n/a 8880 24
3081.2.dp \(\chi_{3081}(17, \cdot)\) n/a 8880 24
3081.2.du \(\chi_{3081}(77, \cdot)\) n/a 8880 24
3081.2.dv \(\chi_{3081}(212, \cdot)\) n/a 8856 24
3081.2.dy \(\chi_{3081}(74, \cdot)\) n/a 8856 24
3081.2.dz \(\chi_{3081}(4, \cdot)\) n/a 4488 24
3081.2.ee \(\chi_{3081}(154, \cdot)\) n/a 8976 48
3081.2.ef \(\chi_{3081}(89, \cdot)\) n/a 17760 48
3081.2.eg \(\chi_{3081}(58, \cdot)\) n/a 8928 48
3081.2.eh \(\chi_{3081}(11, \cdot)\) n/a 17712 48
3081.2.ek \(\chi_{3081}(5, \cdot)\) n/a 17760 48
3081.2.el \(\chi_{3081}(34, \cdot)\) n/a 8928 48
3081.2.eo \(\chi_{3081}(2, \cdot)\) n/a 17712 48
3081.2.ep \(\chi_{3081}(7, \cdot)\) n/a 8976 48

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3081))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3081)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(79))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(237))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1027))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3081))\)\(^{\oplus 1}\)